Qualitative Properties of Steady-State Poisson-Nernst-Planck Systems:
Mathematical Study
By: J.-H. Park and J.W. Jerome
We examine qualitative properties of solutions of self-consistent
Poisson-Nernst-Planck (PNP) systems, including uniqueness.
In the case of vanishing permanent charge, the predominant case studied,
our results unveil a rich structure inherent in these systems, one that is
determined by the boundary conditions and the signs of the
oppositely charged carrier fluxes.
A particularly significant special case, that of simple boundary
conditions, is shown to lead to uniqueness, and to a complete
characterization.
This case underlies the more complicated cases studied later.
A contraction mapping principle is included for
completeness, and allows for an arbitrary permanent charge distribution.
This paper has appeared: SIAM J. Appl. Math. 57 (1997), 609--630.
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